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Trapezoidal footing is a type of footing that holds unequal loads from 2 columns when the heaviest load outside the column distance is restricted.

It is utilized when the area of footing is fixed and the soils at the site are loose soil.

### 1. Formula for Calculating Trapezoidal Footing Volume

As we know, Trapezoidal footing is made by the superimposing of a rectangular cuboid and truncated pyramid as shown in the figure below. Now,

The volume of trapezoidal footing=Volume of Rectangular cuboid (V1)  +  Volume of a truncated pyramid (V2)

= V1 + V2       …………….(Eq.1) I. Volume of rectangular cuboid (V1);

= A * B * hc    …………….(Eq.2 )

where,

A= length of the cuboid

hc= Height of cuboid

II. Volume of a truncated pyramid ( V2 );

= ht/3 * ( A1 + A2 + √(A1 +A2) )  ……..(eq.3)

Where,

A1= area of the bottom surface of the truncated pyramid

A2= area of the upper surface of the pyramid

ht= height of the pyramid

From equations 1,2 and 3, we can write the final  formula for calculating the volume of  trapezoidal footing as shown below;

= V1 + V2

= ( A*B*hc)  + ht/ 3 ( A1 + A2 + (√ (A1+A2)) ) Now, We are going to find out the volume of trapezoidal footing shown in Figure 3 above;

i. ht= 300mm = 0.3m

ii. hc= 300mm=0.3m (let us assume)

iii. Area of cuboid (A *B)= (2000 mm * 1600 mm) = 3.2 m²

iv. Area of the bottom surface of the pyramid(A1) =3.2m²

v. Area of the top surface of the pyramid (A2)= (800*800) mm2 =0.64m²

Now,

Total Volume= V1 + V2

=( A*B*hc)  + ht/ 3 ( A1 + A2 + (√ (A1+A2)) )

=(3.2 * 0.3) + 0.3/3 (3.2+0.64 +(√(3.2+0.64)))

=0.96 +0.57995

= 1.539959 m3

The total volume of the trapezoidal footing in figure 3 = 1.5399m3

### 3. Uses

Trapezoidal footing’s uses are as follows:

I. For residential houses and buildings.

II. When the load applied is uneven or unequal.

III. The soil at the site is loose.

The advantages of trapezoidal footing are as follows:

a. Concrete uses are less.

b. Cheap to construct.

c. Less reinforcement is needed.

The disadvantages of trapezoidal footing are as follows:

a. Good for small buildings only.

b. Chance of settlement.

c. Foundation subjected to pull out, torsion, moment.

### 6. References

1. Content Filter & Authenticity Checking Team, Dream Civil International

(Our team checks every content & detail to maintain quality.)

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Tell us how we can improve this post? Er. Madhu Krishna Poudel ( Founder )
Madhu Krishana Poudel is a distinguished Civil Engineer with extensive experience in site supervision, estimation, and AutoCAD 2D and 3D design. Holding a Bachelor's degree in Civil Engineering from Pokhara University, his work and expertise have earned recognition in reputable sources such as USA Today, Time, Wikipedia, and TheRichest, establishing his credibility and trustworthiness in the construction industry.
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